I'm not sure what the point of it would be .... right now the reason someone logs in is to create/edit blog posts or make other changes in the control panel. There's two roles setup for this -- Administrator and Editor.

If a person leaves a comment, for example, the name, email address, website they enter is saved in a cookie so the next time they are viewing a post, this information is pre-filled for them.

Well, for one thing, can't they put anything in the email address? Most sites these days will verify a user email address by emailing them a link to confirm.

Allowing users to create their own account (as sites like this one do) provides a fairly open format, while still allowing some degree of being able to remove or disable accounts. Yeah, they could create another account, but it requires more effort and if
email addresses must be unique, they'll need another email address if their first account was just disabled.

Okay. BlogEngine is a blog. Not a forum system. Of course lots of things out there exist, but usually for leaving comments on peoples blogs, email address validation doesn't take place. You just leave the comment ... and it either
appears right away, or after it's been moderated by someone.

Yes, BE does have comment moderation. Somewhere on the Settings tab in the control panel, you can turn it on.

If you're logged into the blog and leave a comment (either a test comment or a real comment), the comment will automatically be approved. But for other people on the site who are not logged in, their comment will not show up until you approve it.

There's an extension named "Send Comment Mail" (control panel, Extensions tab) that is enabled by default. When it is enabled, you'll receive an email notification when someone leaves a comment -- to alert you a comment needs to be approved.
Just make sure your email settings are setup. Again, with this too, I think if you're logged into the blog when leaving a comment, this comment notification email isn't sent. So when testing things out, it's best to log out of the blog.